An oven is set at 176.8°C. Marla increases the temperature by 23.8°C.

What is the final oven temperature?

Answer:

6/10 of a mile in one hour

Step-by-step explanation:

3.25 ÷ 5.5 = 0.59 or approx 0.6 miles

Answer:

48

Step-by-step explanation:

Answer:

  (c)  2

Step-by-step explanation:

The dilation scale factor multiplies the distance from the center of dilation.

We are given that QA = 1.25, and that AA' = 1.25. By the segment sum theorem, we have ...

  QA' = QA +AA'

  QA' = 1.25 +1.25 = 2.50

The scale factor multiplies the original distance:

  QA' = k·QA . . . . . . . . . . where k is the dilation scale factor

  2.50 = k·1.25 . . . . . . . . using the known lengths

  2.50/1.25 = k = 2 . . . . divide by the coefficient of k

The scale factor is 2.

Answer:

The election of 1860  established the Democratic and Republican parties as the majority parties in the United States. It also confirmed deep tensions  surrounding slavery and states’ rights between the North and South. Before Lincoln’s inauguration, eleven Southern states seceded from the Union and just after his swearing-in, the Confederate Army fired on Fort Sumter, starting the Civil War.

Answer:

165 degrees Celsius

Step-by-step explanation:

Answer:

18.36 to nearest hundredth.

Step-by-step explanation:

base of the triangle = 1/3 * 32 = 16.

x^2 = 9^2 + 16^2

x^2 = 81 + 256 =  337

x = √337 = 18.36.

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: slope \:\: of \:\: line = \cfrac{3}{2}\)

____________________________________

\( \large \tt Solution \: : \)

The equation of line is written in slope - intercept form

\(\qquad \tt \rightarrow \: f(x) = \dfrac{3}{2} x - 4\)

if we compare it with general slope - intercept equation of line :

\(\qquad \tt \rightarrow \: f(x) = mx + c\)

[ m represents slope of line ]

\(\qquad \tt \rightarrow \: m = \dfrac{3}{2} \)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

\(\frac32\)

Step-by-step explanation:

Hello!

An equation of a line is usually written in slope-intercept form.

Slope Intercept Form: \(y = mx + b\)

If we compare our given equation with the format:

This means that \(\frac32\) would be our slope for the line.

Step-by-step explanation:

i can give you a hint

1)divide into two triangles

2) then find each angle

3) use sine laws to find sides

Answer:

Shelly can be a CrossFit member is 8 Months

($60-900) / $120 = Months

Step-by-step explanation:

Joining the gym costs 60$ so that would be your first month, it then costs $120 every month after. So we would start by subtracting $60 from the total $900

$60 - $900 = $840

Next you would divide your remaning money ($840) by the amount of money it cost per month ($120).

$840 / $120 = 7 Months

7 months plus the Enitial Month

The total number of months that Shelly can be a CrossFit member is 8 Months.

Answer: 3c - 5

Step-by-step explanation:

Since c represent the number of cookies that Mark made. We are then informed that Peter made five less than triple as many cookies as Mark. This will be:

= (3 × c) - 5

= 3c - 5

The expression is 3c - 5

A. In the alternate universe, the p subshell would have 5 orbitals.

B. In the alternate universe, the d subshell would have 10 orbitals.

In the alternate universe where the possible values of mℓ range from -l-1 to l+1, the number of orbitals in each subshell can be determined.

A. For the p subshell, the value of l is 1. Therefore, the range of mℓ would be -1, 0, and 1. Including the additional values of -2 and 2 from the alternate universe, the total number of orbitals in the p subshell would be 5 (mℓ = -2, -1, 0, 1, 2).

B. For the d subshell, the value of l is 2. In the conventional universe, the range of mℓ would be -2, -1, 0, 1, and 2, resulting in 5 orbitals. However, in the alternate universe, the range would extend to -3 and 3. Including these additional values, the total number of orbitals in the d subshell would be 10 (mℓ = -3, -2, -1, 0, 1, 2, 3).

Therefore, in the alternate universe, the p subshell would have 5 orbitals, and the d subshell would have 10 orbitals.

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Answer:

b

Step-by-step explanation:

The proportion of the rise to the run for each of the similar slope triangles is given by:

h / b = mh' / mb' = mh / b

What is proportion?

A proportion is a statement that two ratios or fractions are equal. It is commonly written in the form of two fractions separated by an equal sign, such as a/b = c/d.

To write a proportion comparing the rise to the run for each of the similar slope triangles, we can use the fact that the ratio of corresponding sides of similar triangles is the same.

Let's say we have two similar triangles with corresponding sides of length a, b, and c, and a', b', and c', respectively. Then we can write the following proportion:

a / a' = b / b' = c / c'

Now, let's apply this to finding the proportion of the rise to the run for each of the similar slope triangles.

In a right triangle, the slope is defined as the ratio of the rise (vertical change) to the run (horizontal change). Let's say we have two similar right triangles with slopes m and m', respectively, and the rise and run of the first triangle are h and b, respectively. The rise and run of the second triangle are then mh and mb', respectively.

We can write the proportion of the rise to the run for each triangle as:

h / b = mh' / mb'

Simplifying this proportion, we can cancel out the common factor of b:

h / b = mh' / mb'

h / 1 = mh' / m'

h = bmh'

Therefore, the proportion of the rise to the run for each of the similar slope triangles is given by:

h / b = mh' / mb' = mh / b

The numeric value of this proportion will depend on the specific values of the rise and run for each triangle and the slope of the triangles.

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Answer: The height of an object can be determined using the relationship between the height of an object, the length of its shadow, and the length of a reference shadow. This relationship is given by the formula:

Height of object = (Height of reference object x Length of object's shadow) / Length of reference shadow

Given that a 4-ft vertical post casts a 10-in shadow at the same time a nearby cell phone tower casts a 125-ft shadow, we can use this formula to find the height of the cell phone tower:

Height of the cell phone tower = (4 ft x 10 in) / 125 ft

To find the height of the cell phone tower, we have to convert the 10 inches to feet, since the reference object's height is in feet.

10 inches = 10/12 ft = 5/6 ft

Height of the cell phone tower = (4 ft x 5/6 ft) / 125 ft

Height of the cell phone tower = 20/125 ft = 16/125 ft = 128/1025 ft = 128/1025 * 12/12 in = 128/85 ft

So the cell phone tower is 128/85 ft or (128/85) * 12 = 128/7 ft = 18.285714 ft tall.

The cell phone tower's height is 18.285714 ft.

Step-by-step explanation:

The first 4 terms are 4 ,16,36 and 64 of the sequence (bn)n>=1 of partial sums of the sequence.

To find the first 4 terms of the sequence (bn)n≥1, we will calculate the partial sums as follows:

1. b1 = 4 (the first term)
2. b2 = b1 + 12 = 4 + 12 = 16 (sum of the first two terms)
3. b3 = b2 + 20 = 16 + 20 = 36 (sum of the first three terms)
4. b4 = b3 + 28 = 36 + 28 = 64 (sum of the first four terms)

So, the first 4 terms of the sequence (bn)n≥1 are 4, 16, 36, 64.

Now let's determine a recursive definition for bn. Notice that the difference between each term in the original sequence is 8 (12 - 4, 20 - 12, and 28 - 20). So, we can write the recursive definition as:

bn = bn-1 + 8n, for n > 1, and b1 = 4 (the first term).

This recursive definition can be used to find any term in the sequence (bn)n≥1 of partial sums.

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Answer:

-2x-3

Step-by-step explanation:

6x-7-8x+4

6x-8x=-2x

-7+4=-3

-2x-3

Answer:

-2x-3

Step-by-step explanation:

The dimensions of original lawn are a. 4 feet by 4 feet.

As per the equation and information mentioned in question, x represents the dimension of original lawn. The equation in question represents the relation between area of lawn at side of reduced lawn and it's area. We will solve this equation to find the value of x.

\((x - 8)^{2} = 144\)

The expression on Left Hand Side is same as \((a - b)^{2}\). We know, on expansion, we write it as \(a^{2} + b^{2} - 2ab\). Thus, new equation will be -

\(x^{2} + 8^{2} - 2*x*8 = 144\)

\(x^{2} + 64 + 16x = 144\)

\(x^{2} + 16x + 64 - 144 = 0\)

\(x^{2} + 16x - 80 = 0\)

\(x^{2} + 20x - 4x - 80 = 0\)

x (x + 20) -4 (x + 20) = 0

(x + 20) (x - 4) = 0

So, the two values of x that we get are:

x = 4 and -20.

The dimensions of lawn can not be negative. Hence, the value of x will be x.

Therefore, the dimensions of original lawn are a. 4 feet by 4 feet.

The complete question is -

Jillian is trying to save water, so she reduces the size  of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation \((x - 8)^{2} = 144\), x represents the side measure of the original lawn. What were the dimensions of the original lawn?

a. 4 feet by 4 feet

b. 8 + \(6\sqrt{2}\) feet by 8 + \(6\sqrt{2}\) feet

c. 8 - \(6\sqrt{2}\) feet by 8 + \(6\sqrt{2}\) feet

d. 20 feet by 20 feet

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(a) The wave function Ψ(x, t) is normalized if ∫ |Ψ(x, t)|^2 dx = 1, Substituting the wave function into the integral, we get ∫ |Acos(πx/a)|^2 dx = 1.

Using the trigonometric identity |cos(x)|^2 = 1/2(1 + cos(2x)), we can rewrite the integral as ∫ 1/2(1 + cos(2πx/a)) dx = 1.

The integral on the left-hand side can be evaluated using the integral given in the problem, which gives us

1/2(4/1 + 2(a/π)x) = 1.

Solving for A, we get A = √2/a.

The condition that must be satisfied for A to be truly a constant is that γ must be real. This is because the wave function Ψ(x, t) must be a solution to the time-independent Schrödinger equation, which requires that the coefficient of the exponential term be real.

(b) The probability that a measurement of the particle's position x at time t yields a result within the range |x(t)| < a/6 is given by

=∫ |Ψ(x, t)|^2 dx |x| < a/6.

Substituting the wave function into the integral, we get

∫ |Acos(πx/a)|^2 dx |x| < a/6.

Using the trigonometric identity |cos(x)|^2 = 1/2(1 + cos(2x)), we can rewrite the integral as ∫ 1/2(1 + cos(2πx/a)) dx |x| < a/6.

The integral on the left-hand side can be evaluated using the integral given in the problem, which gives us

1/2(4/1 + 2(a/π)x) |x| < a/6.

This integral can be evaluated numerically. For example, if a = 1, then the integral is equal to 0.954.

(d) The potential V(x, t) is given by V(x, t) = 1/Ψ(x, t) [ih ∂t∂Ψ(x, t) + 2mh 2 ∂x 2∂ 2Ψ(x, t)].

Substituting the wave function into the expression for V(x, t), we get

V(x, t) = 1/[Acos(πx/a)exp(γt)] [ihγAcos(πx/a)exp(γt) + 2mh 2π 2Asin(πx/a)exp(γt)].

Simplifying the expression, we get

V(x, t) = (ihγ + 2mh 2π 2)Asin(πx/a)exp(γt).

For |x| < a/6, the value of the sine term is approximately equal to 1, so the potential V(x, t) is approximately equal to

V(x, t) = (ihγ + 2mh 2π 2)A.

The value of the constant A can be determined by normalizing the wave function, as shown in part (a). For example, if a = 1 and γ = 1, then A = √2/a = √2. In this case, the potential V(x, t) is approximately equal to

V(x, t) = (ih + 4π 2)√2.

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

Step-by-step explanation:

m∠APE = 4x + 14

m∠DPE = (4x + 8) - (2x + 11) = 2x - 3

(4x+4)+(4x+8)+(4x+4)+(2x+11)+(2x-3) = 360

16x + 24 = 360

16x = 360 - 24 = 336

x = 335/16 = 21

A)  m∠APE = 4(21) + 4 = 88

B)  m∩ED = 2(21) - 3 = 39

C)  m∩BCD = (4(21) + 4) + (2(21) + 11) = 141

The two triangles ΔRST and ΔUVW are similar to each other by the SAS property.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

Given that there are two triangles ΔRST and ΔUVW. ΔRST has the angle ∠T = 59° and the sides RT = 15 units and ST = 13 units. The other triangle ΔWVU has the angle ∠W = 59° and the sides WV= 52 units and WU= 60 units.

Firstly the two angles are the same,

∠T= ∠W = 59°

The two sides are dilated by a scale factor of 4,

WV /  ST = 52 / 13 = 4

WU /  RT = 60 / 15 = 4

So these sides are similar.

Hence, from the SAS property, the two triangles are similar.

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Answer: Semi-regular tessellations are made of more than one kind of regular polygon. There are only 8 semi-regular tessellations.

A semi-regular tessellation is a tiling of the plane using regular polygons where the arrangement at each vertex is the same but the types of polygons may vary.

There are 8 known semi-regular tessellations.

There is a finite number of possibilities due to the constraints on the arrangements of polygons.

We have,

A semi-regular tessellation, also known as a uniform tessellation or Archimedean tessellation, is a type of tessellation or tiling of the plane where regular polygons are used to fill the space.

In a semi-regular tessellation, the arrangement of polygons at each vertex is the same, but the types of polygons may vary.

To create a semi-regular tessellation, two conditions must be met:

- Each vertex (or corner) of the tessellation must have the same arrangement of polygons around it.

- The sequence of polygons around each vertex must be the same, although the actual polygons may differ.

There are exactly 8 known semi-regular tessellations, which are formed using regular polygons.

These tessellations include combinations of triangles, squares, hexagons, and dodecagons (12-sided polygons). Some examples of semi-regular tessellations include the honeycomb pattern and the tiling known as "Truchet tiles."

As for the question of why there aren't infinitely many semi-regular tessellations, it is because the arrangement and combination of regular polygons at each vertex are constrained.

The conditions for a semi-regular tessellation limit the possibilities for the types and arrangements of polygons. While there are many ways to arrange polygons around a vertex, the number of distinct arrangements is finite.

Thus,

A semi-regular tessellation is a tiling of the plane using regular polygons where the arrangement at each vertex is the same but the types of polygons may vary.

There are 8 known semi-regular tessellations, and there is a finite number of possibilities due to the constraints on the arrangements of polygons.

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Answer:

B. 8 • 8 • 8 • 8 • 8

Step-by-step explanation:

I'm gonna assume you meant 8 to the 5th power, or \(8^5\).

Step 1: Define and explain.

Remember: exponents are simply repeated multiplication.

Exponents tell you how many times to multiply the base number by itself.

---------------------------------------------------

---------------------------------------------------

Step 2: Solve.

\(base-8\)

\(exponent-5\)

\(8^5=8*8*8*8*8\)

Step 3: Conclude.

Therefore, \(8^5\) is the same as \(8*8*8*8*8.\)

Answer:

B

Step-by-step explanation:

Answer:

(10, -2)

Step-by-step explanation:

The inequalities are:

y < x - 7               (1)

y < (1/5)x - 2        (2)

To solve this problem, we have to solve both equations simultaneously and then find the value of x and y that makes the inequality true.

To solve the inequality, subtract inequality (2) from inequality (1) which gives:

0 < (4/5) x - 5

-(4/5)x < -5

Dividing both sides of the equation by -4/5 gives:

-(4/5)x / (-4/5) < -5/ (-4/5)

x > 6.25

Put x > 6.2 in inequality 1

y < 6.25 - 7

y < -0.75

The solution of the inequality is x > 6.25 and y < -0.75

From the list of option, the correct answer is (10, -2) since 10 > 6.25 and -2 < -0.75

The probability mass function of the discrete random variable x is:

p(x = -2) = 1/3

p(x = -1) = 1/6

p(x = 0) = 1/6

p(x = 1) = 1/6

p(x = 2) = 1/3

To determine the value of a, we first need to confirm that the probability mass function satisfies the two conditions of a valid probability mass function:

For this probability mass function, the possible values of x are -2, -1, 0, 1, and 2. Therefore, we can calculate the sum of probabilities as:

p ( x = -2 ) + p ( x = -1 ) + p ( x = 0) + p (x = 1) + p (x = 2)

= \(|(-2)| \times a + |(-1)| \times a + |0| \times a + |1| \times a + |2| \times a\)

= 2a + a + 0 + a + 2a

= 6a

To satisfy the first condition of a valid probability mass function, the sum of probabilities must be equal to 1. Therefore, we can set up the equation:

6a = 1

a = 1/6

Thus, the value of a that satisfies the conditions of a valid probability mass function is a = 1/6. Therefore, the probability mass function of the discrete random variable x is:

p(x = -2) = 1/3

p(x = -1) = 1/6

p(x = 0) = 1/6

p(x = 1) = 1/6

p(x = 2) = 1/3

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The value of the integral by reversing the order of integration is (81/4)(96e^(12) - 1).

We need to evaluate the integral of 3y over the region R bounded by x=0, x=3, y=27, and y=6e^(4x) by reversing the order of integration.

To reverse the order of integration, we first draw the region of integration, which is a rectangle. Then, we integrate with respect to x first. For each value of x, the limits of integration for y are from 27 to 6e^(4x). Thus, we have:

∫(0 to 3) ∫(27 to 6e^(4x)) 3y dy dx = ∫(27 to 6e^(12)) ∫(0 to ln(y/6)/4) 3y dx dy

To find the new limits of integration for x, we solve y=6e^(4x) for x to get x=ln(y/6)/4. The limits of integration for y are still from 27 to 6e^(12).

Now, we can evaluate the integral using the reversed order of integration:

∫(27 to 6e^(12)) (∫(0 to ln(y/6)/4) 3y dx) dy = ∫(27 to 6e^(12)) (3y/4 ln(y/6)) dy

Integrating this expression gives:

(3/4)(y ln(y/6) - (9/4)y) from y=27 to y=6e^(12) = (81/4)(96e^(12) - 1)

Therefore, the value of the integral by reversing the order of integration is (81/4)(96e^(12) - 1).

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The graph of equation y=-4(x+3) - 2 is as shown below.

In this question we have been given an equation y=-4(x+3) - 2

We need to graph an equation y=-4(x+3) - 2

For x = 0,

y = -4(0+3) - 2

y = -14

For x = 1,

y = -4(1+3) - 2

y = -18

For x = -1,

y = -4(-1+3) - 2

y = -10

The line y=-4(x+3) - 2 passes through points (0, -14), (1, -18) and (-1, -10)

The graph of equation y=-4(x+3) - 2 is as shown below.

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